In the previous paper [1]}, we gave a prescription
to construct a set of string products with an \(L_\infty \)  structure required
by complete action of the type II superstring field theory by extending
the asymmetric construction proposed in [2]}.
It is sufficient for defining an action and gauge transformation
but is slightly complicated and could not be mapped to those in the WZW-like
formulation. In this paper, we propose another prescription by extending
the symmetric construction in [2]}.
